You cannot change your name unless you do a true reset, or so people thought.

I copied this from Wikia because they explain it better then I could, and I'm too lazy to type it all out.

1. Go into C:\Users\YourName\AppData\Local\UNDERTALE within Windows (~/Library/Application Support/com.tobyfox.undertale/ For Mac)

2. Open the file named "file0" with Notepad (any other programs similar to Notepad should work.)

3. The name is stored on the first line. Replace it with a new name. Numbers and symbols can be added to this new name, but if it is longer than 6 characters, it will cover surrounding text. Using a forbidden name has no effect.

Have fun making your name whatever you want!